An optical phase modulation device for modulating a phase of an input light signal at a modulation frequency is provided, which can be used in integrated photonics applications. The device can include an optical phase modulator, for example a thermo-optic phase shifter having an effective refractive index that depends linearly temperature, configured to impart a phase shift to the input light signal, the phase shift varying quadratically in response to an applied modulating electric drive signal. The device can also include a phase modulator driver configured to apply the electric drive signal to the optical phase modulator, the electric drive signal having a time-varying component oscillating at half the modulation frequency and no time-constant component, thereby imparting the phase shift, modulated at the modulation frequency, to the phase of the input light signal to produce a phase-modulated light signal. Optical phase modulation systems and methods are also disclosed.
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19. A method of modulating a phase of an input light signal at a modulation frequency, the method comprising:
receiving the input light signal in an optical phase modulator configured to impart a phase shift to the input light signal, the phase shift varying quadratically with an applied drive voltage or electric current; and
applying the drive voltage or electric current to the optical phase modulator as an electric drive signal, the electric drive signal having a time-varying component oscillating at half the modulation frequency and no time-constant component, thereby imparting the phase shift, modulated at the modulation frequency, to the phase of the input light signal to produce a phase-modulated light signal.
10. An optical phase modulation device for modulating a phase of an input light signal at a modulation frequency, the optical phase modulation device comprising:
an optical phase modulator configured to receive and impart a phase shift to the input light signal, the phase shift varying quadratically with an applied drive voltage or electric current; and
a phase modulator driver configured to apply the drive voltage or electric current to the optical phase modulator as an electric drive signal having a time-varying component oscillating at half the modulation frequency and no time-constant component, thereby imparting the phase shift, modulated at the modulation frequency, to the phase of the input light signal to produce a phase-modulated light signal.
1. An optical phase modulation system, comprising:
a light source assembly configured to emit an input light signal;
an optical phase modulator comprising:
a modulating waveguide section for receiving and supporting propagation of the input light signal, the modulating waveguide section having an effective refractive index that depends linearly on temperature; and
a resistive heater in thermal contact with the modulating waveguide section; and
a phase modulator driver configured to apply a drive voltage or electric current having a time-varying component oscillating at half the modulation frequency and no time-constant component to the resistive heater to generate heat that is transferred into the modulating waveguide section, thereby changing the effective refractive index, and in turn, the phase of the input light signal propagating therealong to produce a phase-modulated light signal modulated at the modulation frequency.
14. An optical phase modulation device for modulating a phase of an input light signal at a modulation frequency, the optical phase modulation device comprising:
an optical phase modulator comprising:
a modulating waveguide section for receiving and supporting propagation of the input light signal, the modulating waveguide section having an effective refractive index that depends linearly on temperature; and
a resistive heater in thermal contact with the modulating waveguide section; and
a phase modulator driver configured to apply a drive voltage or electric current having a time-varying component oscillating at half the modulation frequency and no time-constant component to the resistive heater to generate heat that is transferred into the modulating waveguide section, thereby changing the effective refractive index, and in turn, the phase of the input light signal propagating therealong to produce a phase-modulated light signal modulated at the modulation frequency.
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This application claims the benefit of U.S. Provisional Patent Application No. 62/715,371 filed on Aug. 7, 2018. The entire teachings of the above application are incorporated herein by reference.
The technical field generally relates to the field of optics, and more particularly, to optical phase modulation methods and systems.
Optical phase modulation is employed to control the phase of a light signal in a wide range of telecommunication and sensing applications. Non-limiting fields of application include coherent optical communications using, for example, the phase-shift key (PSK) modulation format or its derivatives; fiber optics and integrated photonics; fiber optic gyroscope sensors and other interferometric-based sensors; lidar and other optical remote sensing techniques; and active mode locking of lasers. Common types of phase modulators are thermo-optic and electro-optic phase modulators, which achieve phase modulation of a light signal via, respectively, thermally and electrically controlled changes in the refractive index of the medium in which the light signal travels. While these types of optical phase modulators have proven useful in some applications, they also have some drawbacks and limitations, for example in terms of achieving control over the harmonic content of the phase-modulated signal. Challenges therefore remain in the field of optical phase modulation.
The present description generally relates to techniques for modulating the phase of an input light signal at a desired modulation frequency to produce a phase-modulated light signal with reduced harmonic content, particularly in terms of the second harmonic at twice the desired modulation frequency. The control over the harmonic content of the phase-modulated light signal can be achieved by driving the optical phase modulator with a modulating electric drive signal having a time-domain waveform with certain characteristics.
In some implementations, the present techniques can be used in silicon-based photonic integrated circuits or other types of planar lightwave circuits. In other implementations, the present techniques can be used in optical fiber communication systems. In yet other implementations, the present techniques can be implemented in phase modulators used for laser frequency stabilization.
In accordance with another aspect, there is provided an optical phase modulation device for modulating a phase of an input light signal at a modulation frequency, the optical phase modulation device including:
In accordance with another aspect, there is provided an optical phase modulation device for modulating a phase of an input light signal at a modulation frequency, the optical phase modulation device including:
In accordance with another aspect, there is provided an optical phase modulation system, including:
In accordance with another aspect, there is provided an optical phase modulation system, including:
In some implementations, the optical phase modulation system can include more than one light source defining the light source assembly. For example, in one embodiment, the light source assembly can include a master laser and one or more slave lasers implemented as a multifrequency laser source assembly provided in an integrated photonics platform. In such a case, the optical phase modulator can be provided in the output path of the master laser or the slave laser(s) to produce a phase-modulated output signal. For example, the optical phase modulator can be provided in the path used to distribute the master laser signal to the optical phase-locked loop (OPLL) of the slave laser(s). When the OPLL has a large amount of gain at the common modulation frequency, the present techniques can allow generating slave-laser output signals having substantially the same phase modulation as the master output signal. In some applications, such a multifrequency laser source assembly can be part of a fiber optic gyroscope or a phase-modulated RF-over-fiber link with interferometric detection.
In accordance with another aspect, there is provided an optical phase modulator for phase-modulating an input light signal at a modulation frequency, the optical phase modulator having a phase modulation function that depends quadratically on an applied drive voltage or electric current, and being configured, upon the applied drive voltage or electric current being provided as an electric drive signal having a time-varying component oscillating at half the modulation frequency and no time-constant component, to produce, from the input light signal, a phase-modulated light signal modulated at the modulation frequency in accordance with the phase modulation function.
In some implementations, the optical phase modulator is a thermo-optic phase shifter configured to modulate the input light signal based on the thermo-optic effect, according to which a change in temperature results in a change in the refractive index of the optical guiding medium in which the input light signal travels as it passes through the thermo-optic phase shifter. The change in refractive index induces a change in the phase of the input light signal, which produces the phase-modulated light signal. In such implementations, the electric drive signal—that is, the drive voltage or electric current—applied to the thermo-optic phase shifter by the phase modulator driver generates heat, predominantly by Joule heating. The heat thus generated is delivered to the thermo-optic phase shifter, changes its temperature, and induces, via the thermo-optic effect, a corresponding change in the refractive index of the thermo-optic material forming the optical guiding medium. In Joule heating, the temperature change experienced by the optical guiding medium is proportional to the square of the drive voltage or electric current applied by the phase modulator driver.
In some implementations, the thermo-optic phase shifter includes:
In some implementations, the optical phase modulator is embodied by an electro-optic phase shifter. The electro-optic phase-shifter can be configured to modulate the input light signal based on a quadratic electro-optic effect, for example the Kerr electro-optic effect, according to which a change in the refractive index of the optical guiding medium in which the input light signal travels as it passes through the thermo-optic phase shifter is proportional to the square of an applied electric field.
In addition to thermo-optic and electro-optic phase shifters, the present techniques may, in principle, be implemented with or in any suitable type of electrically drivable phase modulator whose phase modulation function depends linearly on the square of the drive voltage or electric current, or equivalently, linearly on the electric power input supplied by the phase modulator driver.
In some implementations, more than one optical phase modulator may be provided in cascade, each applying a phase shift to the light signal passing therethrough, thereby adding a combined phase shift to the input light signal that produces a desired phase-modulated light signal. In other implementations, the present techniques may additionally or alternatively be configured so that the light signal makes more than one pass through one or more optical phase modulators.
In accordance with an aspect, there is provided a method of modulating a phase of an input light signal at a modulation frequency, the method including:
In some implementations, the electric drive signal is a bipolar sinusoidal signal with no direct current (dc) offset. In such a case, the phase-modulated light signal is phase modulated sinusoidally with respect to the input light signal. However, electric drive signals having non-sinusoidal, periodic or quasi-periodic, time-domain waveforms may be used in other implementations.
In accordance with another aspect, there is provided a method of modulating a phase of an input light signal at a modulation frequency, the method including:
In accordance with another aspect, there is provided a method of modulating a phase of an input light signal at a modulation frequency, the method including:
It is to be noted that other method and process steps may be performed prior to, during or after the steps described herein. The order of one or more steps may also differ, and some of the steps may be omitted, repeated and/or combined, depending on the application.
Other objects, features and advantages of the present description will become more apparent upon reading of the following non-restrictive description of specific embodiments thereof, given by way of example only with reference to the appended drawings. Although specific features described in the above summary and in the detailed description below may be described with respect to specific embodiments or aspects, it should be noted that these specific features can be combined with one another unless stated otherwise.
In the present description, similar features in the drawings have been given similar reference numerals. To avoid cluttering certain figures, some elements may not be indicated if they were already identified in a preceding figure. It is appreciated that the elements of the drawings are not necessarily depicted to scale, since emphasis is placed on clearly illustrating the elements and structures of the present embodiments. Furthermore, positional descriptors indicating the location and/or orientation of one element with respect to another element are used herein for ease and clarity of description. Unless otherwise indicated, these positional descriptors should be taken in the context of the figures and should not be considered limiting. It will be understood that such spatially relative terms are intended to encompass different orientations in the use or operation of the present embodiments, in addition to the orientations exemplified in the figures.
Unless stated otherwise, the terms “connected”, “coupled”, and derivatives and variants thereof, refer to any connection or coupling, either direct or indirect, between two or more elements. The connection or coupling between the elements may be, for example, mechanical, optical, electrical, thermal, logical, or a combination thereof.
In the present description, the terms “a”, “an” and “one” are defined to mean “at least one”, that is, these terms do not exclude a plural number of items, unless stated otherwise.
Terms such as “substantially”, “generally”, “about”, and “nearly”, that modify a value, condition or characteristic of a feature of an exemplary embodiment, should be understood to mean that the value, condition or characteristic is defined within tolerances that are acceptable for the proper operation of this exemplary embodiment for its intended application.
The terms “linear dependence” and “quadratic dependence”, and derivatives and variants thereof, when referring to the relationship between two quantities, are meant to encompass not only exact or strict linear and quadratic dependencies, but also generally, substantially, approximately, nearly or sufficiently linear and quadratic dependencies. The terms “linear dependence” and “quadratic dependence” are therefore intended to cover scenarios where the relationship between a first quantity and a second quantity can be considered “linear” or “quadratic”, to a given tolerance, within the operational range of an exemplary embodiment.
The term “sinusoidal” is meant to encompass not only pure sine and cosine waveforms, but also waveforms that are substantially or approximately sinusoidal, to a given tolerance, within the operational range of an exemplary embodiment. It will be appreciated that, in a given embodiment, the exact shape of the electric drive signal generated by the phase modulator driver can somewhat differ from that of an exact mathematical representation of a sine or cosine waveform, yet be sufficiently close to it to be considered as such for practical purposes.
The present description relates to optical phase modulation techniques for modulating a phase of an input light signal to produce a phase-modulated light signal modulated at a desired modulation frequency with reduced harmonic content. In accordance with various non-limiting aspects, the present description relates to a phase-modulating method; an optical phase modulator; an optical phase modulation device including an optical phase modulator and a phase modulator driver; and an optical phase modulation system including a light source assembly, an optical phase modulator, and a phase modulator driver.
In some implementations, the present techniques use a thermo-optic phase modulator configured to impart a phase shift that depends linearly on temperature to the input light signal. In such implementations, the present techniques involve electrically driving the thermo-optic phase modulator with a time-varying drive voltage or electric current, thereby generating heat by Joule effect to change the phase of the input light signal and output a phase-modulated light signal. In the present description, the expression “drive voltage or electric current” is sometimes shortened to “electric drive signal” for conciseness. Because Joule heating scales quadratically with an applied voltage or electric current, the phase shift imparted by the thermo-optic phase modulator varies linearly with the square of the electric drive signal, or equivalently, linearly with the electric power input supplied by the phase modulator driver. As described in greater detail below, in some implementations, obtaining a phase-modulated light signal modulated at a modulation frequency fm with reduced second harmonic content at 2fm, involves using an electric drive signal having a time-varying component oscillating at half the modulation frequency, ½fm, and no time-constant component, to account for the quadratic relationship between the phase shift imparted by the thermo-optic phase modulator and the electric drive signal applied thereto.
The present techniques can be useful in various applications where it is desirable or required to produce a phase-modulated light signal in which the second harmonic at twice the modulation frequency is suppressed or substantially reduced. For example, the present techniques can be implemented in a wide range of applications including, but not limited to, optical fiber communications; integrated photonics; fiber optic gyroscope sensors and other interferometric sensing techniques; lidar and other optical remote sensing techniques; active mode locking of lasers; and laser frequency stabilization.
Particularly, some embodiments of the present techniques can be implemented, at least partly, in a silicon-based or another high-index-contrast photonic platform including a plurality of planar optical waveguides provided in an integrated circuit configuration. It should be noted, however, that the present techniques are not limited to silicon photonics and other integrated photonics applications, and that they can be used in various other contexts, for example in optical fiber-based applications.
In the present description, the term “optical waveguide” or simply “waveguide” is used to refer to a device or structure that directs, constrains or guides electromagnetic radiation to flow along a light-guiding path defined by the waveguide. Non-limiting examples of optical waveguides include photonic waveguides, for example in planar lightwave circuits, optical fibers, and photonic crystals.
In the present description, the terms “light” and “optical” are used to refer to radiation in any appropriate region of the electromagnetic spectrum. The terms “light” and “optical” are therefore not limited to visible light, but can include, for example, the infrared wavelength range. For example, in some implementations, the light signal that is modulated can have wavelengths ranging from about 400 nanometers (nm) to about 2 micrometers (μm), although the present techniques may operate beyond this range.
Referring to
In some implementations, one or more components of the optical phase modulation system 20 may be part of a photonic integrated circuit, for example based on silicon-on-insulator (SOI) technology, and may be implemented in any appropriate type of planar waveguide structure. Non-limiting examples of planar waveguide structures include slab waveguides, strip waveguides, ridge waveguides, and rib waveguides. SOI technology refers to an integrated circuit technology that uses a layered silicon-insulator-silicon substrate rather than a conventional silicon substrate. The thin layer of silicon formed on top of the insulating layer, typically silica, can be patterned to define one or more waveguides, in accordance with a given circuit design. However, the present techniques are not limited to SOI technology but may be based on various other types of layered materials such as, for example, silicon nitride (Si3N4), silicon carbide (SiC), silicon oxynitride (SiOxN), silicon oxide (SiOx), indium phosphide (InP), gallium arsenide (GaAs), polymers and the like. The general principles underlying the structure and optical properties of SOI-based and other conventional integrated photonic circuits are known in the art and need not be covered in detail herein.
The light source assembly 26 can be embodied by any appropriate device or combination of devices adapted to generate an input light signal 22 which can be phase-modulated according to the present techniques to produce the phase-modulated light signal 24. Non-limiting examples of possible light sources can include a gas laser, a solid-state laser, a diode laser, a dye laser, a fiber laser, and a non-laser source such as a light-emitting diode. Depending on the application, the one or more light sources of the light source assembly 26 may be operated in a continuous-wave or pulsed regime. The choice and number of light sources can be dictated by various factors including, but not limited to, the operating wavelength, the peak power, the degree of coherence, the spatial and spectral profiles, the space requirements, and for a pulsed light source, the pulse characteristics. As noted above, in some embodiments, the light source assembly 26 can be configured to emit the input light signal 22 in a waveband ranging from about 400 nm to about 2 μm.
In SOI-based photonics implementations, the light source assembly 26 may be configured to deliver the input light signal 22 into the input optical waveguide 28 either indirectly (e.g., by transmitting light from an off-chip external laser source through an optical fiber, followed by the coupling of the fiber mode into the SOI waveguide) or directly (e.g., by hybrid/heterogeneous integration of III-V laser device/material on the silicon photonic integrated circuit platform, followed by the coupling of the laser mode into the SOI waveguide). Each of the indirect and direct coupling techniques can be further characterized by the employed coupling approach, such as edge-coupling, grating-coupling and evanescent-coupling. In either case, the input light signal 22 emitted by the light source assembly 26 may be coupled into the input optical waveguide 28 using an appropriate optical coupler, or coupling device or mechanism, schematically represented by reference character 40 in
In the illustrated embodiment, the input optical waveguide 28 is depicted, for simplicity, as a single waveguiding structure that extends continuously between the optical coupler 40 and the optical phase modulator 30, but more complex waveguiding structures can also be used. For example, in some embodiments, the input optical waveguide 28 can include a plurality of waveguide sections coupled together by a variety of passive components (e.g., splitters, couplers, filters, and mode adapters) and/or active components (e.g., modulators, switches, and detectors).
In some implementations, the electric field of the input light signal 22 may have a sinusoidal time-dependent component represented by the expression:
Ei(t)=Ei0 sin(ωit), (1)
where Ei0 is the amplitude and ωi=2πfi is the angular frequency, with fi the frequency. It should be noted that while the input light signal 22 in Equation (1) is assumed to be sinusoidal for simplicity, this is not meant to be limiting and non-sinusoidal signals may be used in other implementations.
The optical phase modulator 30 receives the input light signal 22 from the input optical waveguide 28. The optical phase modulator 30 is configured, upon being driven with the electric drive signal 34 applied by the phase modulator driver 32, to add a time-dependent phase shift or offset, ϕm(t), to the input light signal 22, and to produce the phase-modulated light signal 24 modulated at a desired modulation frequency fm. In other words, the phase shift ϕm(t) is the time-dependent phase term that varies when imparting the phase modulation. If the input light signal 22 is given by Equation (1), the time-dependent component of the electric field of the phase-modulated light signal 24 may be expressed as:
Em(t)=Ei0 sin [ωit+ϕm(t)], (2)
where the phase shift ϕm(t) is time-varied at the desired modulation frequency fm. In some implementations, the modulation frequency fm can range up to the gigahertz (GHz) frequency range. For example, when the optical phase modulator 30 is a thermo-optic phase shifter, the modulation frequency fm can range between 100 hertz (Hz) and 5 to 10 megahertz (MHz), particularly between 1 kilohertz (kHz) and 150 kHz. As described in greater detail below, the phase-shift ϕm(t) applied to the input light signal 22 through the optical phase modulator 30 can vary quadratically with the electric drive signal 34.
In general, the phase of a light wave is directly proportional to the optical path length traveled by the light wave. The optical path length is the product of the effective refractive index n of the medium in which the light travels times the physical length L of the path through the medium. Phase modulation techniques can rely on a change in either the refractive index (e.g., as in thermo-optic and electro-optic phase modulators) or the physical length (e.g., as in piezoelectric phase modulators) of the medium, or in both. In the former case, the phase shift ϕm resulting from a refractive index variation Δn, assumed spatially uniform across the length L of the medium for simplicity, may be expressed as:
where λi is the operating wavelength.
In some implementations, the optical phase modulator 30 is a thermo-optic phase shifter. The thermo-optic phase shifter can be configured to modulate the input light signal 22 based on a thermo-optic effect, in which a change in temperature results in a change in the refractive index of the optical guiding medium in which the input light signal travels as it passes through the thermo-optic phase shifter. It is noted that due to the strong thermo-optic coefficient, α, of silicon at typical telecommunication wavelengths and at room temperature, phase modulators based on the thermo-optic effect are commonly used in silicon-based photonics.
In the illustrated embodiment, the optical phase modulator 30 is a thermo-optic phase shifter that includes a modulating waveguide section 42 for supporting propagation of the input light signal 22 received from the input optical waveguide 28, and a resistive heater 44 in thermal contact with the modulating waveguide section 42, for example via one or more thermal bridges 46. For example, the modulating waveguide section 42 can be made of silicon, and the resistive heater 44 can be made of metal, doped semiconductor or another suitable conductive material. Upon being supplied with the electric drive signal 34, the resistive heater 44 generates heat 48, including by Joule heating. The heat 48 thus generated is transferred to the modulating waveguide section 42, changing its refractive index in accordance with a change in temperature and, in turn, the phase of the input light signal 22 propagating therealong to produce the phase-modulated light signal 24. Depending on the application, a variety of thermo-optic phase shifter configurations are known in the art and can be used to implement the optical phase modulation techniques disclosed herein. Non-limiting examples of thermo-optic phase shifter configurations include thermal phase shifters, thermal phase modulators, and metal heaters integrated in silicon photonics platforms.
Assuming that the refractive index n depends linearly, or nearly linearly, on temperature T, such that a change in temperature, ΔT, results in a directly proportional change in refractive index, Δn≅αΔT, where a is constant over ΔT, then the phase shift ϕm in Equation (3) can be written in terms of ΔT as follows:
It should be noted that at least for relatively small temperature variations, the assumption of a linear relationship between refractive index and temperature generally holds in typical thermo-optical phase shifters used in silicon-based photonic circuits and silica-based optical fibers.
In the illustrated embodiment, since the heat 48 transferred to the modulating waveguide section 42 by the resistive heater 44 is generated predominantly by Joule heating, the temperature change experienced by the former is proportional to the square of the electric drive signal 34 supplied to the latter by the phase modulator driver 32, if the heat coupling efficiency between the resistive heater 44 and the modulating waveguide section 42 is sufficiently independent, or only weakly dependent, on temperature. In this case, assuming that the electric drive signal 34 is a drive voltage V or electric current I, Equation (4) can be expressed in terms of V and I as follows:
where Zth is the impedance associated with the resistive heater 44, such that ΔT=V2/Zth=ZthI2. Then, if the electric drive signal 34 is a time-varying modulation function, V(t) or I(t), Equation (2) may be expressed in terms of V(t) and I(t) as follows:
Em(t)=Ei0 sin [ωit+AVV2(t)], (6a)
Em(t)=Ei0 sin [ωit+AII2(t)], (6b)
where AV=(2παL/λiZth) and AI=(2παLZth/λi).
It is appreciated from Equations (5a)-(5b) and (6a)-(6b) that the phase shift ϕm applied to the input light signal 22 through the optical phase modulator 30 depends quadratically on the electric drive signal 34, V or I, supplied by the phase modulator driver 32. This quadratic relationship between ϕm and V or I may pose some challenges in applications where it is required or desirable that the phase modulation imposed by the optical phase modulator 30 be linearly proportional to the drive voltage or electric current and/or that the phase-modulated light signal 24 fulfill certain spectral purity requirements, for example related to the undesirable or deleterious presence of harmonics in the spectrum of the phase-modulated light signal 24 at integer multiples of the desired modulated frequency fm, notably the second harmonic at 2fm. As such, the choice of the modulation waveform of the electric drive signal 34 applied to the optical phase modulator 30 by the phase modulator driver 32 may have an impact on the spectrum of the phase-modulated light signal.
For example, in some implementations, it may be required or desirable to produce a phase-modulated light signal 24 which is phase modulated sinusoidally at a desired modulation frequency fm, by the optical phase modulator 30, as controlled by the electric drive signal 34, V(t) or I(t), applied by the phase modulator driver 32. In such a case, Equation (2) for the time-dependent component of the electric field of the phase-modulated light signal 24 may be expressed as:
Em(t)∝Ei0 sin [ωit+ϕm0 sin(ωmt)], (7)
where ωm=2πfm is the angular modulation frequency. To achieve such a sinusoidal phase modulation, a variety of time-domain modulation waveform could be used for the electric drive signal 34 applied by the phase modulator driver 32.
For example, one could consider generating the electric drive signal 34 as a unipolar drive voltage V(t) expressed as:
V(t)=V0+Vm(t)=V0+Vm0 sin(ωmt), with V0>Vm0, (8)
where V0 is the time-constant, or direct current (dc), component of V(t), and Vm=Vm0 sin(ωmt) is the time-varying, or alternating current (ac), component of V(t). Given that V0>Vm0, V(t) remains strictly positive, hence the designation “unipolar”. The time-varying phase shift ϕm(t) imparted by this drive voltage can be found as follows:
Equation (9) indicates that the resulting time-varying phase shift ϕm(t) includes a time-constant component, AV(V02+½Vm02), a fundamental component, 2AVV0Vm0 sin(ωmt), modulated at the desired modulation frequency fm, and a second harmonic component, −½AV Vm02 cos (2ωmt), at twice the modulation frequency, 2fm. In such a case, the ratio of the second harmonic component to the fundamental component is given by:
which may not be negligible and may become adversely or undesirably large in some applications having more stringent requirements in terms of spectral purity or reduced harmonic content of the phase-modulated light signal.
The present techniques provide the electric drive signal 34 with a time-domain waveform having certain characteristics that aim to reduce the harmonic content, particularly the second harmonic, of a phase-modulated light signal 24 given by Equations (6a)-(6b), that is, a phase-modulated light signal 24 whose time-varying phase modulation function, ϕm(t), varies quadratically with a time-varying modulating drive voltage, V(t), or electric current, I(t). Particularly, in the disclosed embodiments, the electric drive signal 34, V(t), has a time-varying component, Vm(t) or Im(t), oscillating at half the modulation frequency, ½fm, and no time-constant component, that is, V0=0 and I0=0. For example, in the case of a sinusoidal phase modulation, such a drive voltage V(t) may be written as:
V(t)=Vm(t)=Vm0 sin(½ωmt). (11)
This type of electric drive signal 34 can be referred to as a bipolar drive voltage with zero dc offset, the designation “bipolar” reflecting the fact that the electric drive signal 34 includes both positive and negative voltage values.
The time-varying phase shift ϕm(t) imparted by the bipolar drive voltage of Equation (11) can be found as follows:
ϕm(t)=AVV2(t)=AV[Vm0 sin(½ωmt)]2=½AVVm02[1−cos(ωmt)]. (12)
Referring to
It can be appreciated from Equation (12) that the resulting time-varying phase shift ϕm(t) includes a time-constant component, ½AVVm02, a fundamental component, −½AVVm02 cos(ωmt), modulated at the desired modulation frequency, but no second harmonic component. In such a case, the ratio of the second harmonic component to the fundamental component is given by:
Equation (13) indicates that the phase modulation function ϕm(t) obtained according to Equation (12) will have, in theory, no second or higher-order harmonics. In practice, it is appreciated that the spectral purity of the phase modulation may be limited by the intrinsic nonlinearities of the optical phase modulator. These nonlinearities can be due to a nonuniform temperature distribution along the modulating waveguide section 42 resulting from a nonuniform heat transfer from the resistive heater 44. Additionally, or alternatively, these nonlinearities can result from the dependence between the temperature of the resistive heater 44 and the amplitude of the electric drive signal 34 deviating non-negligibly from a pure quadratic response, for example if the resistance of the resistive heater 44 varies as a function of temperature within its operating range. Referring to
It should be noted that with respect to the electric drive signal applied by the phase modulator driver, the expression “oscillating at half the modulation frequency”, and variants and derivative thereof, are meant to encompass not only “exactly” oscillating at half the modulation frequency, but also “generally”, “substantially”, “approximately”, “nearly” or “sufficiently” oscillating at half the modulation frequency. Likewise, the expression “no time-constant component”, and variants and derivative thereof, are meant to encompass not only “exactly” no time-constant component, but also “generally”, “substantially”, “approximately”, “nearly” or “sufficiently” no time-constant component. The terms “oscillating at half the modulation frequency” and “no time-constant component” are therefore intended to cover scenarios where the electric drive signal can be considered to have a time-varying component that oscillates at half the desired modulation frequency and no time-constant component within tolerances that are acceptable for proper operation or application of a given exemplary embodiment.
Returning to
By setting and adjustment of the electric drive signal 34, the phase modulator driver 32 provides control over the parameters of the phase modulation imposed on the input light signal 22 by the optical phase modulator 30, for example in terms of the desired modulation waveform, modulation frequency, and/or amplitude. In some implementations, the operation of the phase modulator driver 32 may be synchronized, fully or partly, with the operation of the light source assembly 26.
Returning to
It should be noted that while the above-described examples are based on sinusoidal modulation time-domain waveforms, for simplicity, this is not meant to limit the scope of the present techniques, which can be implemented with a non-sinusoidal, periodic or nearly periodic, electric drive signals.
It should also be noted that while some implementations of the present techniques can be implemented with a thermo-optic phase modulator, other implementations could additionally or alternatively use another type of electrically drivable phase modulator whose phase modulation function depends linearly on the square of the drive voltage or electric current.
For example, referring to
Referring to
The system 20 of
The system 20 further includes a fiber resonator 60 in optical communication with the master laser 52 and the slave laser 54. The fiber resonator 60 is configured to receive, in a first direction, a signal 62 originating from the master laser 52 and, in a second direction opposite the first direction, a modulated signal 64 from the slave laser 54. From these counterpropagating signals 62, 64, the fiber resonator 60 is configured to generate, based on the Sagnac effect, an error signal allowing discrimination of a frequency detuning between the frequency of the slave laser 54 and a resonance frequency of the fiber resonator 60.
It is appreciated that RFOG systems, notably using master-slave laser setups, are generally known in the art, and need not be described in greater detail herein. Reference can be made, for example, to U.S. Pat. No. 8,923,352 B2 and U.S. Pat. No. 9,587,945 B2, the entire contents of which are incorporated herein by reference.
Referring to
The system 20 of
Of course, numerous modifications could be made to the embodiments described above without departing from the scope of the appended claims.
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